Fractional Design (Polar)

A polar-coordinate pattern generator — build stars, circles, spirals, or entirely custom polar curves by defining an angle list and a radial list as fractions. Each vertex is (angleFraction × 2π, radialFraction × Nominal Radius), and a per-vertex travel flag lets you lift the nozzle for disconnected shapes. Pick a shape preset as a starting point, then tweak the lists by hand.

See Predefined Models for the general workflow and how to select this model.

Parameters (sliders)

Parameters

Nominal Radius: Base radius in mm (5–80). All radial fractions are multiplied by this value. Sets the overall size of the pattern.
Shape Preset: Populates the Angle/Radial/Travel lists automatically: Star, Double Star, Circle, or Coarse Spiral. Pick one as a starting point, then edit the lists manually if you want a custom shape.
Angle Fractions: List of 2–50 angle fractions between 0 and 1 (where 1 = 360°). Each entry defines the angular position of one vertex.
Radial Fractions: List of 2–50 radial fractions between 0 and 1. Each entry defines the radius of the matching vertex as a fraction of Nominal Radius.
Travel Moves: List of 0/1 flags, one per vertex. 0 = extrude to this vertex, 1 = travel (pen up). Use travels to jump between disconnected shapes in one toolpath.
Layers: Number of layers to stack (1–10). Each layer repeats the same polar pattern at an increasing Z height.
Quantity: Number of parts generated side by side in one job (1–5).

How it works

For each vertex i, the point is (r, θ) = (radialFractions[i] × Nominal Radius, angleFractions[i] × 2π).
Consecutive vertices are connected with either an extruded line (travel = 0) or a travel move (travel = 1).
Layers re-walks the same path at increasing Z — good for building up structure or for solid printed patterns.
The three lists must have the same length. Selecting a Shape Preset refills all three in one go so they stay consistent.